In chiral materials,
translational and rotational motions are coupled with each other [1]}.
However,
in our model,
the coupling between
the translational and rotational states of an electron
is mediated by the nuclear vibrational modes
belonging to the \(\mathrm {e}_1\)  and \(\mathrm {e}_2\)  representation.
Indeed,
the product representation \(\mathrm {e}_i \times \mathrm {E}_i\)  for \(i=1,2\)  includes \(\mathrm {A}\)  representation.
Consequently, there arises a finite matrix element \(*{\mathrm {A}}{\mathrm {e}_i}{\mathrm {E}_i}\)  in a symbolic form.
The nuclei in the \(\mathrm {e}_{1,2}\)  representation also induce the coupling
between the rotational states.
This coupling between degenerate rotational states
causes the spontaneous distortion,
which is known as the Jahn-Teller effect [2]}, [3]}.
The coupling between non-degenerate (\(\mathrm {E}_i\)  and \(\mathrm {A}\) ) states,
can also cause a similar symmetry-breaking called the pseudo Jahn-Teller effect [2]}, [3]}.
The nuclear coordinates in the \(\mathrm {e}_{1,2}\)  representation
are written as
\(Q_\pm = \rho e^{\pm i \varphi }\)  with the radius \(\rho \)  and the angle \(\varphi \) .
The symmetry operations transform \(Q_\pm \) 
in the following way:
\(C_3 Q_\pm = e^{\pm i 2\pi /3} Q_\pm ,\) 
